Report

Lecture 19 Satellites Quick Review • Newton’s Law of gravity Gm1m2 F1on 2 (r ) F2on1 (r ) 2 r 2 11 N m G 6.67 *10 2 kg Circular Orbits • M is mass of parent and m the mass of the satellite. M>>m GMm m v2 FM on m (r ) 2 mac r r GM v r 2 3 4 2 T r GM • Kepler’s Law Geostationary Satellite • At the equator, how far above the earth’s surface should a satellite orbit so it stays overhead? • Rearth = 6.37 x 106 m • G=6.67 x 1011 N•m2/kg2 Mearth = 5.98 x 1024 kg A cyclist goes around a level, circular track at constant speed. Since the cyclist’s speed is constant, her 50% 50% acceleration is constant se Fa l Tr ue 1. True 2. False QUIZ • A motor cycle is in a loop-the-loop. At the top of the loop… • A) Draw a free body diagram • B) What is the minimum speed the motor cycle must have if the radius of the loop is 15. m? Homework due Friday • Problems: 6: 24, 25, 27, 29, 33, 44, 45, 51, 58, 59 Problem 6:27 • What is the ratio between the sun’s gravitational force on you and the earth’s gravitational force on you? • Rearth = 6.37 x 106 m • G=6.67 x 1011 N•m2/kg2 Mearth = 5.98 x 1024 kg Rearth-sun =1.5 x 1011 m Msun = 1.99x1030 kg Problem 6:27 cont • Take ratio Fsun Fearth GM sun m 2 R 2 earth sun M sun Rearth 2 GM earth m M earth Rearth sun 2 Rearth 2 1.99*10 6.37 *10 4 6.0*10 24 11 5.98*10 1.5*10 30 6 6:33 The space shuttle is in an orbit 250 miles high. What are its orbital period (in minutes) and orbital speed? Rearth = 6.37 x 106 m G=6.67 x 10-11 N•m2/kg2 Mearth = 5.98 x 1024 kg 1 mi = 1.609 km 2 4 2 T GM 3 r 6:33 • 250 mi *1.609km/mi=326.5 km • r= 6.37 x 106 m+3.265 x 105 m =6.70 x 106 • T=5.46 x 103 s = 90.9 minutes 6:44 • A 5g coin is placed 15cm from the center of a turntable. µs = 0.80, µk = 0.50. As turntable starts from rest and speeds up to 60 rpm, does coin slide off? mv 2 f s s ,required mg r 60rpm f 1 Hz 60s / m s ,required 2 f .15* 2 *1 v r .604 rg rg 9.8 2 2 2 So coin does not slip 2 6:45 Conical Pendulum Find T, ω 1.0m T θ r=0.20m m r FNET , x T cos r FNET , y w T sin 0 .2 0 cos 78.46 1 1 W=mg 2 6:51 Ultracentrifuge R=0.10 m 70,000 rpm Δm= 10 mg = 0.000010 kg What is net force? r a 6:58 Martian geostationary satellite What are its speed and altitude? dayMars:=24.8 hours 6:59 g on Mars, Maximum walking speed? g MARS G * M MARS 2 RMARS vMAX gr r .70m